Pulse compression waveforms and processing techniques for high-resolution signature formation are typically constrained by hardware limitations and target motion. This paper serves as a summary comparison of three modern pulse compression techniques: (1) linear frequency modulation (matched filtering), (2) stretch processing, and (3) stepped frequency waveforms, that are designed to perform under different hardware limitations. However, trade-offs exists between the three techniques which limit range window sizes, result in range aliasing, define minimum sampling rates and instantaneous bandwidths, and define range-Doppler ambiguities and distortions. This paper focuses on the mathematical development of the three techniques and relates the results to hardware requirements and range-Doppler ambiguities/distortions.